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Analysis of a frictional contact problem for viscoelastic materials with long memory
1.  Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Computer Science, ul. Łojasiewicza 6, 30348 Krakow, Poland, Poland 
2.  Laboratoire de Mathématiques et Physique pour les Systèmes, Université de Perpignan, 52 Avenue Paul Alduy, 66860 Perpignan 
References:
[1] 
F. H. Clarke, "Optimization and Nonsmooth Analysis," Wiley, Interscience, New York, 1983. 
[2] 
Z. Denkowski, S. Migórski and N. S. Papageorgiou, "An Introduction to Nonlinear Analysis: Theory," Kluwer Academic/Plenum Publishers, Boston, Dordrecht, London, New York, 2003. 
[3] 
Z. Denkowski, S. Migórski and N. S. Papageorgiou, "An Introduction to Nonlinear Analysis: Applications," Kluwer Academic/Plenum Publishers, Boston, Dordrecht, London, New York, 2003. 
[4] 
A. D. Drozdov, "Finite Elasticity and Viscoelasticity  A Course in the Nonlinear Mechanics of Solids," World Scientific, Singapore, 1996. 
[5] 
G. Duvaut and J. L. Lions, "Inequalities in Mechanics and Physics," SpringerVerlag, Berlin, 1976. 
[6] 
C. Eck, J. Jarušek and M. Krbec, "Unilateral Contact Problems: Variational Methods and Existence Theorems," Pure and Applied Mathematics, 270, Chapman/CRC Press, New York, 2005. 
[7] 
W. Han and M. Sofonea, "Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity," American Mathematical Society, International Press, 2002. 
[8] 
I. R. Ionescu, C. Dascalu and M. Campillo, Slipweakening friction on a periodic system of faults: Spectral analysis, Z. Angew. Math. Phys. (ZAMP), 53 (2002), 980995. doi: 10.1007/PL00012624. 
[9] 
I. R. Ionescu, Q.L. Nguyen and S. Wolf, Slip displacement dependent friction in dynamic elasticity, Nonlinear Analysis, 53 (2003), 375390. doi: 10.1016/S0362546X(02)003024. 
[10] 
S. Migórski, Hemivariational inequality for a frictional contact problem in elastopiezoelectricity, Discrete Continuous Dynam. Syst. Ser. B, 6 (2006), 13391356. doi: 10.3934/dcdsb.2006.6.1339. 
[11] 
S. Migórski, A. Ochal and M. Sofonea, Integrodifferential hemivariational inequalities with applications to viscoelastic frictional contact, Mathematical Models and Methods in Applied Sciences, 18 (2008), 271290. doi: 10.1142/S021820250800267X. 
[12] 
Z. Naniewicz and P. D. Panagiotopoulos, "Mathematical Theory of Hemivariational Inequalities and Applications," Marcel Dekker, Inc., New York, Basel, Hong Kong, 1995. 
[13] 
P. D. Panagiotopoulos, "Hemivariational Inequalities, Applications in Mechanics and Engineering," SpringerVerlag, Berlin, 1993. 
[14] 
A. D. RodríguezAros, M. Sofonea and J. M. Viaño, A class of evolutionary variational inequalities with Volterratype integral term, Mathematical Models and Methods in Applied Sciences, 14 (2004), 555577. 
[15] 
M. Shillor, M. Sofonea and J. J. Telega, "Models and Analysis of Quasistatic Contact," Lecture Notes Physics, 655, Springer, Berlin, Heidelberg, 2004. 
[16] 
M. Sofonea and A. Matei, "Variational Inequalities with Applications. A Study of Antiplane Frictional Contact Problems," Advances in Mechanics and Mathematics, 18, Springer, New York, 2009. 
[17] 
M. Sofonea, A. D. RodríguezAros and J. M. Viaño, A class of integrodifferential variational inequalities with applications to viscoelastic contact, Mathematical and Computer Modelling, 41 (2005), 13551369. doi: 10.1016/j.mcm.2004.01.011. 
[18] 
E. Zeidler, "Nonlinear Functional Analysis and Applications II A/B," Springer, New York, 1990. 
show all references
References:
[1] 
F. H. Clarke, "Optimization and Nonsmooth Analysis," Wiley, Interscience, New York, 1983. 
[2] 
Z. Denkowski, S. Migórski and N. S. Papageorgiou, "An Introduction to Nonlinear Analysis: Theory," Kluwer Academic/Plenum Publishers, Boston, Dordrecht, London, New York, 2003. 
[3] 
Z. Denkowski, S. Migórski and N. S. Papageorgiou, "An Introduction to Nonlinear Analysis: Applications," Kluwer Academic/Plenum Publishers, Boston, Dordrecht, London, New York, 2003. 
[4] 
A. D. Drozdov, "Finite Elasticity and Viscoelasticity  A Course in the Nonlinear Mechanics of Solids," World Scientific, Singapore, 1996. 
[5] 
G. Duvaut and J. L. Lions, "Inequalities in Mechanics and Physics," SpringerVerlag, Berlin, 1976. 
[6] 
C. Eck, J. Jarušek and M. Krbec, "Unilateral Contact Problems: Variational Methods and Existence Theorems," Pure and Applied Mathematics, 270, Chapman/CRC Press, New York, 2005. 
[7] 
W. Han and M. Sofonea, "Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity," American Mathematical Society, International Press, 2002. 
[8] 
I. R. Ionescu, C. Dascalu and M. Campillo, Slipweakening friction on a periodic system of faults: Spectral analysis, Z. Angew. Math. Phys. (ZAMP), 53 (2002), 980995. doi: 10.1007/PL00012624. 
[9] 
I. R. Ionescu, Q.L. Nguyen and S. Wolf, Slip displacement dependent friction in dynamic elasticity, Nonlinear Analysis, 53 (2003), 375390. doi: 10.1016/S0362546X(02)003024. 
[10] 
S. Migórski, Hemivariational inequality for a frictional contact problem in elastopiezoelectricity, Discrete Continuous Dynam. Syst. Ser. B, 6 (2006), 13391356. doi: 10.3934/dcdsb.2006.6.1339. 
[11] 
S. Migórski, A. Ochal and M. Sofonea, Integrodifferential hemivariational inequalities with applications to viscoelastic frictional contact, Mathematical Models and Methods in Applied Sciences, 18 (2008), 271290. doi: 10.1142/S021820250800267X. 
[12] 
Z. Naniewicz and P. D. Panagiotopoulos, "Mathematical Theory of Hemivariational Inequalities and Applications," Marcel Dekker, Inc., New York, Basel, Hong Kong, 1995. 
[13] 
P. D. Panagiotopoulos, "Hemivariational Inequalities, Applications in Mechanics and Engineering," SpringerVerlag, Berlin, 1993. 
[14] 
A. D. RodríguezAros, M. Sofonea and J. M. Viaño, A class of evolutionary variational inequalities with Volterratype integral term, Mathematical Models and Methods in Applied Sciences, 14 (2004), 555577. 
[15] 
M. Shillor, M. Sofonea and J. J. Telega, "Models and Analysis of Quasistatic Contact," Lecture Notes Physics, 655, Springer, Berlin, Heidelberg, 2004. 
[16] 
M. Sofonea and A. Matei, "Variational Inequalities with Applications. A Study of Antiplane Frictional Contact Problems," Advances in Mechanics and Mathematics, 18, Springer, New York, 2009. 
[17] 
M. Sofonea, A. D. RodríguezAros and J. M. Viaño, A class of integrodifferential variational inequalities with applications to viscoelastic contact, Mathematical and Computer Modelling, 41 (2005), 13551369. doi: 10.1016/j.mcm.2004.01.011. 
[18] 
E. Zeidler, "Nonlinear Functional Analysis and Applications II A/B," Springer, New York, 1990. 
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